Janos Bolyai was born on December 15, 1832 in Hungary. His father was a famous mathematician as well who tried to prove or disprove Eucild's parallel postulate. Him and his father, Farkas Bolyai were unsuccessful in replacing the parallel postulate, however they discovered the basics of Hyperbolic geometry. Bolyai tried to spread his ideas in Marosvásárhely with his father, however his father was not supportive of Janos' ideas of geometry. Janos tried to speak to his former teacher for help, however, he was again, unsuccessful. After waiting for a response from any famous mathematicians, his own father realized, that his son created something useful in mathematics and encouraged his to publicize an Appendix. Farkas invited his son back to Marosvásárhely where he published an Appendix which included foundations of what is known as Euclidean, Hyperbolic and absolute geometry today.
Janos Bolyai was acknowledged after that by Gauss as well who was considered Bolyai's work similar to his own. Janos also developed a detailed geometric concept of complex numbers as ordered pairs of real numbers. He died of pnemonia at the age of 57 and left 20,000 pages of the Appendix unpublished. This work is currently in Bolyai-Teleki library in Tirgu-Mures.
Janos Bolyai was acknowledged after that by Gauss as well who was considered Bolyai's work similar to his own. Janos also developed a detailed geometric concept of complex numbers as ordered pairs of real numbers. He died of pnemonia at the age of 57 and left 20,000 pages of the Appendix unpublished. This work is currently in Bolyai-Teleki library in Tirgu-Mures.
Information from: http://www.gap-system.org/~history/Biographies/Bolyai.html